User:BetterVotingAdvocacy/Negative vote-counting approach for pairwise counting: Difference between revisions
User:BetterVotingAdvocacy/Negative vote-counting approach for pairwise counting (view source)
Revision as of 23:02, 15 February 2022
, 2 years ago→Table for pairwise counting method performance comparison
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*For both regular counting approaches, a lower bound has been provided (when N=R), and since there is no upper bound, instead the number of marks required when N is one higher than R is provided.
*For both negative and semi-negative counting, the numbers provided are a series that include both lower and upper bounds on the number of marks that have to be made, depending on N (which starts at R, and sequentially increases by one, up to twice that i.e. 2R), and how last-ranked candidates are counted.
**For example: when R is 2 and N is 2, negative pairwise counting only requires 1 tally mark to be made; but when N goes up to 3 (or higher), negative pairwise counting requires 3 tally marks.
Here is a pairwise counting table demonstrating the performance measures shown in the above table (ballot tallied is A>B>C>D>E, and ranks only 5 out of a maximum of 10 candidates in election):
{| class="wikitable"
|+Negative pairwise counting values ''italicized'', regular approach values <big>big</big>, and modified regular approach values bolded
!
!A
!B
!C
!D
!E
!F
!G
!H
!I
!J
|'''''<small>1 ballot</small>'''''
|<big>1</big>
|<big>1</big>
|<big>1</big>
|<big>1</big>
|<big>1</big>
|<big>1</big>
|<big>1</big>
|<big>1</big>
|<big>1</big>
|-
|B
|''<small>-1</small>''
|''<small>1 ballot</small>''
|'''<big>1</big>'''
|'''<big>1</big>'''
|'''<big>1</big>'''
|'''<big>1</big>'''
|'''<big>1</big>'''
|'''<big>1</big>'''
|'''<big>1</big>'''
|'''<big>1</big>'''
|-
|C
|''<small>-1</small>''
|''<small>-1</small>''
|''<small>1 ballot</small>''
|'''<big>1</big>'''
|'''<big>1</big>'''
|'''<big>1</big>'''
|'''<big>1</big>'''
|'''<big>1</big>'''
|'''<big>1</big>'''
|'''<big>1</big>'''
|-
|D
|''<small>-1</small>''
|''<small>-1</small>''
|''<small>-1</small>''
|''<small>1 ballot</small>''
|'''<big>1</big>'''
|'''<big>1</big>'''
|'''<big>1</big>'''
|'''<big>1</big>'''
|'''<big>1</big>'''
|'''<big>1</big>'''
|-
|E
|''<small>-1</small>''
|''<small>-1</small>''
|''<small>-1</small>''
|''<small>-1</small>''
|''<small>1 ballot</small>''
|'''<big>1</big>'''
|'''<big>1</big>'''
|'''<big>1</big>'''
|'''<big>1</big>'''
|'''<big>1</big>'''
|}
* Note that 5 rows of the table (that were at the bottom) have been omitted because they are left empty in all pairwise counting methods. Note that negative counting is faster when voters rank only a few of all candidates, and potentially slower otherwise.
For example, a voter who votes A>B when there are 10 candidates can be assumed to vote for A and B in every matchup, except they don't prefer B>A:
| |||